Design of Scheduling Algorithms Using Game Theoretic Ideas

Scheduling a set of jobs over a collection of machines to optimize a certain quality-of-service measure is one of the most important research topics in both computer science theory and practice. In this thesis, we design algorithms that optimize {\em flow-time} (or delay) of jobs for scheduling problems that arise in a wide range of applications. We consider the classical model of unrelated machine scheduling and resolve several long standing open problems; we introduce new models that capture the novel algorithmic challenges in scheduling jobs in data centers or large clusters; we study the effect of selfish behavior in distributed and decentralized environments; we design algorithms that strive to balance the energy consumption and performance.

The technically interesting aspect of our work is the surprising connections we establish between approximation and online algorithms, economics, game theory, and queuing theory. It is the interplay of ideas from these different areas that lies at the heart of most of the algorithms presented in this thesis.

The main contributions of the thesis can be placed in one of the following categories.

1. Classical Unrelated Machine Scheduling: We give the first polygorithmic approximation algorithms for minimizing the average flow-time and minimizing the maximum flow-time in the offline setting. In the online and non-clairvoyant setting, we design the first non-clairvoyant algorithm for minimizing the weighted flow-time in the resource augmentation model. Our work introduces iterated rounding technique for the offline flow-time optimization, and gives the first framework to analyze non-clairvoyant algorithms for unrelated machines.

2. Polytope Scheduling Problem: To capture the multidimensional nature of the scheduling problems that arise in practice, we introduce Polytope Scheduling Problem (\psp). The \psp problem generalizes almost all classical scheduling models, and also captures hitherto unstudied scheduling problems such as routing multi-commodity flows, routing multicast (video-on-demand) trees, and multi-dimensional resource allocation. We design several competitive algorithms for the \psp problem and its variants for the objectives of minimizing the flow-time and completion time. Our work establishes many interesting connections between scheduling and market equilibrium concepts, fairness and non-clairvoyant scheduling, and queuing theoretic notion of stability and resource augmentation analysis.

3. Energy Efficient Scheduling: We give the first non-clairvoyant algorithm for minimizing the total flow-time + energy in the online and resource augmentation model for the most general setting of unrelated machines.

4. Selfish Scheduling: We study the effect of selfish behavior in scheduling and routing problems. We define a fairness index for scheduling policies called {\em bounded stretch}, and show that for the objective of minimizing the average (weighted) completion time, policies with small stretch lead to equilibrium outcomes with small price of anarchy. Our work gives the first linear/ convex programming duality based framework to bound the price of anarchy for general equilibrium concepts such as coarse correlated equilibrium.

Rationale and design of the Exercise Intensity Trial (EXCITE): A randomized trial comparing the effects of moderate versus moderate to high-intensity aerobic training in women with operable breast cancer.

BACKGROUND: The Exercise Intensity Trial (EXcITe) is a randomized trial to compare the efficacy of supervised moderate-intensity aerobic training to moderate to high-intensity aerobic training, relative to attention control, on aerobic capacity, physiologic mechanisms, patient-reported outcomes, and biomarkers in women with operable breast cancer following the completion of definitive adjuvant therapy. METHODS/DESIGN: Using a single-center, randomized design, 174 postmenopausal women (58 patients/study arm) with histologically confirmed, operable breast cancer presenting to Duke University Medical Center (DUMC) will be enrolled in this trial following completion of primary therapy (including surgery, radiation therapy, and chemotherapy). After baseline assessments, eligible participants will be randomized to one of two supervised aerobic training interventions (moderate-intensity or moderate/high-intensity aerobic training) or an attention-control group (progressive stretching). The aerobic training interventions will include 150 mins.wk⁻¹ of supervised treadmill walking per week at an intensity of 60%-70% (moderate-intensity) or 60% to 100% (moderate to high-intensity) of the individually determined peak oxygen consumption (VO₂peak) between 20-45 minutes/session for 16 weeks. The progressive stretching program will be consistent with the exercise interventions in terms of program length (16 weeks), social interaction (participants will receive one-on-one instruction), and duration (20-45 mins/session). The primary study endpoint is VO₂peak, as measured by an incremental cardiopulmonary exercise test. Secondary endpoints include physiologic determinants that govern VO₂peak, patient-reported outcomes, and biomarkers associated with breast cancer recurrence/mortality. All endpoints will be assessed at baseline and after the intervention (16 weeks). DISCUSSION: EXCITE is designed to investigate the intensity of aerobic training required to induce optimal improvements in VO₂peak and other pertinent outcomes in women who have completed definitive adjuvant therapy for operable breast cancer. Overall, this trial will inform and refine exercise guidelines to optimize recovery in breast and other cancer survivors following the completion of primary cytotoxic therapy. TRIAL REGISTRATION: NCT01186367.

Using electronic health record data for substance use Screening, Brief Intervention, and Referral to Treatment among adults with type 2 diabetes: Design of a National Drug Abuse Treatment Clinical Trials Network study.

BACKGROUND: The Affordable Care Act encourages healthcare systems to integrate behavioral and medical healthcare, as well as to employ electronic health records (EHRs) for health information exchange and quality improvement. Pragmatic research paradigms that employ EHRs in research are needed to produce clinical evidence in real-world medical settings for informing learning healthcare systems. Adults with comorbid diabetes and substance use disorders (SUDs) tend to use costly inpatient treatments; however, there is a lack of empirical data on implementing behavioral healthcare to reduce health risk in adults with high-risk diabetes. Given the complexity of high-risk patients' medical problems and the cost of conducting randomized trials, a feasibility project is warranted to guide practical study designs. METHODS: We describe the study design, which explores the feasibility of implementing substance use Screening, Brief Intervention, and Referral to Treatment (SBIRT) among adults with high-risk type 2 diabetes mellitus (T2DM) within a home-based primary care setting. Our study includes the development of an integrated EHR datamart to identify eligible patients and collect diabetes healthcare data, and the use of a geographic health information system to understand the social context in patients' communities. Analysis will examine recruitment, proportion of patients receiving brief intervention and/or referrals, substance use, SUD treatment use, diabetes outcomes, and retention. DISCUSSION: By capitalizing on an existing T2DM project that uses home-based primary care, our study results will provide timely clinical information to inform the designs and implementation of future SBIRT studies among adults with multiple medical conditions.